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    <title>zeropen</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>zeropen</b> -  zero pencil</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[Z,U]=zeropen(Sl)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>Sl</b>
        </tt>: a linear system (<tt>
          <b>syslin</b>
        </tt> list in state-space form <tt>
          <b>[A,B,C,D]</b>
        </tt>)</li>
      <li>
        <tt>
          <b>Z</b>
        </tt>: matrix pencil <tt>
          <b>Z=s*E-A</b>
        </tt>
      </li>
      <li>
        <tt>
          <b>U</b>
        </tt>: square orthogonal matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b>Z = sE - F</b>
      </tt>  is the zero pencil of the linear system <tt>
        <b>Sl</b>
      </tt> with 
    matrices <tt>
        <b>[A,B,C,D]</b>
      </tt>. Utility function.</p>
    <p>
    With <tt>
        <b>U</b>
      </tt> row compression of <tt>
        <b>[B;D]</b>
      </tt> i.e, <tt>
        <b>U*[B;D]=[0;*]</b>
      </tt>; one has:</p>
    <pre>

U*[-sI+A |B;   [ Z |0;      
      C  |D] = [ * |*]
   
    </pre>
    <p>
    The zeros of <tt>
        <b>Z</b>
      </tt> are the zeros of <tt>
        <b>Sl</b>
      </tt>.</p>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../polynomials/systmat.htm">
        <tt>
          <b>systmat</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../linear/kroneck.htm">
        <tt>
          <b>kroneck</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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